Computational complexity reduction for BN2O networks using similarity of states

Although probabilistic inference in a general Bayesian belief network is an NP-hard problem, inference computation time can be reduced in most practical cases by exploiting domain knowledge and by making appropriate approximations in the knowledge representation. In this paper we introduce the property of similarity of states and a new method for approximate knowledge representation which is based on this property. We define two or more states of a node to be similar when the likelihood ratio of their probabilities does not depend on the instantiations of the other nodes in the network. We show that the similarity of states exposes redundancies in the joint probability distribution which can be exploited to reduce the computational complexity of probabilistic inference in networks with multiple similar states. For example, we show that a BN2O network---a two layer networks often used in diagnostic problems---can be reduced to a very close network with multiple similar states. Probabili..